Master Polynomial and Rational Functions: Practice Quizzes and Assessments

Question 1

Find the degree of the polynomial f(x) = 3x^4 - 2x^3 + 5x - 1

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 2

Which transformation shifts the graph of f(x) = x^2 left by 3 units?

Accepted Answer

f(x) = (x - 3)^2

Answer

f(x) = (x + 3)^2

Answer

f(x) = x^2 + 3

Answer

f(x) = x^2 - 3

Question 3

Determine the degree of the polynomial function f(x) = x³ - 2x² + 5x - 1.

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 4

Identify the domain of the rational function f(x) = (x² - 4) / (x - 2).

Accepted Answer

{x | x ≠ 2}

Answer

{x | x ≠ -2}

Answer

{x | x ≠ ±2}

Answer

All real numbers

Question 5

Solve the polynomial equation x^3 - 2x^2 - 5x + 6 = 0.

Accepted Answer

x = 1, x = 2, x = 3

Answer

x = -1, x = -2, x = -3

Answer

x = 2, x = -3, x = 1

Answer

x = -2, x = 3, x = -1

Question 6

Which of the following is the vertical asymptote of the rational function (g(x) = (2x+1)/(x-3))?

Accepted Answer

x=3

Answer

x=1

Answer

x=2

Answer

x=-3

Question 7

Which of the following is a valid way to solve the equation (x + 2)/(x - 1) = 3?

Accepted Answer

Cross-multiply and solve for x.

Answer

Factor the denominator and solve for x.

Answer

Set the numerator equal to zero and solve for x.

Answer

Set the denominator equal to zero and solve for x.

Question 8

What is the sum of the roots of the polynomial function f(x) = x^3 - 4x^2 + 5x - 2?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 9

What is the degree of the polynomial function (f(x) = 3x^4 - 2x^2 + 5x - 1)?

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 10

What is the vertical asymptote of the rational function (f(x) = (x + 2) / (x - 3))?

Accepted Answer

x = 3

Answer

y = 1

Answer

x = -2

Answer

y = 0

Question 11

What is the horizontal asymptote of the rational function (f(x) = (2x^2 + 1) / (x^2 - 4))?

Accepted Answer

y = 2

Answer

x = -2

Answer

y = 1

Answer

x = 2

Question 12

The graph of a rational function has a hole at x = 2. Which of the following could be the function?

Accepted Answer

f(x) = (x^2 - 4) / (x - 2)

Answer

f(x) = (x + 2) / (x - 2)

Answer

f(x) = (x^2 - 4) / (x + 2)

Answer

f(x) = (x - 2) / (x^2 - 4)

Question 13

A rectangular garden is to be enclosed by 100 meters of fencing. If the length is twice the width, what is the area of the garden?

Accepted Answer

500 square meters

Answer

250 square meters

Answer

1000 square meters

Question 14

The function (f(x) = 1 / (x - 1)) is defined for all real numbers except:

Accepted Answer

x = 1

Answer

x = -1

Answer

x = 0

Question 15

What is the degree of the polynomial function f(x) = 2x^3 - 5x^2 + 7x - 1?

Accepted Answer

3

Answer

2

Answer

5

Answer

4

Question 16

What is the leading coefficient of the polynomial f(x) = -x^4 + 3x^2 -2?

Accepted Answer

-1

Answer

1

Answer

2

Answer

3

Question 17

Which of the following could be a factor of the denominator of a rational function that has a removable discontinuity at x = 3?

Accepted Answer

(x - 3)

Answer

(x^2 + 9)

Answer

(x + 3)^2

Answer

(x^2 - 9)

Question 18

Which of the following rational functions has BOTH a vertical asymptote at x = 1 and a horizontal asymptote at y = 2?

Accepted Answer

f(x) = (2x - 2) / (x - 1)

Answer

f(x) = (x - 2) / (x - 1)

Answer

f(x) = (x + 2) / (x - 1)

Answer

f(x) = (2x + 2) / (x - 1)

Question 19

Which of the following functions is a polynomial?

Accepted Answer

f(x) = 2x^3 - 5x + 1

Answer

f(x) = 1 / (x^2 - 4)

Answer

f(x) = 2x^(1/2) + 5

Answer

f(x) = |x| + 3

Question 20

What is the degree of the polynomial f(x) = 3x^4 - 5x^2 + 2?

Accepted Answer

4

Answer

5

Answer

2

Answer

3

Question 21

As x approaches infinity, what is the end behavior of the polynomial function f(x) = -2x^5 + 3x^3 - x?

Accepted Answer

As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.

Answer

As x approaches infinity and negative infinity, f(x) approaches zero.

Answer

As x approaches infinity and negative infinity, f(x) approaches positive infinity.

Question 22

What are the zeros of the polynomial function f(x) = x^2 - 4x + 3?

Accepted Answer

x = 1 and x = 3

Answer

x = -2 and x = -1

Answer

x = 2 and x = 1

Answer

x = -1 and x = -3

Question 23

Which of the following is a rational function?

Accepted Answer

f(x) = (x^2 + 1) / (x - 2)

Answer

f(x) = x^3 + 2x - 1

Answer

f(x) = √(x + 1)

Question 24

What is the vertical asymptote of the rational function f(x) = (x + 1) / (x - 3)?

Accepted Answer

x = 3

Answer

y = -1

Answer

x = -1

Answer

y = 1

Question 25

A company's profit, in dollars, can be modeled by the function P(x) = -x^2 + 100x - 1500, where x represents the number of units sold. How many units must be sold to maximize profit?

Accepted Answer

50

Answer

100

Answer

25

Answer

75

Question 26

Which of the following is a polynomial function?

Accepted Answer

f(x) = 2x³ - 5x² + 7

Answer

f(x) = 2^x

Answer

f(x) = √x + 1

Answer

f(x) = 1/x

Question 27

What is the degree of the polynomial function f(x) = 3x⁴ - 2x² + 1?

Accepted Answer

4

Answer

2

Answer

3

Answer

1

Question 28

What is the end behavior of the polynomial function f(x) = -x³ + 2x² - 3x + 4?

Accepted Answer

As x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.

Answer

As x approaches positive infinity, f(x) approaches positive infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Question 29

Which of the following is a rational function?

Accepted Answer

f(x) = (x² + 1) / (x - 2)

Answer

f(x) = √x + 1

Answer

f(x) = x² + 3x - 4

Question 30

What is the vertical asymptote of the rational function f(x) = (x + 1) / (x - 3)?

Accepted Answer

x = 3

Answer

y = 1

Answer

y = -1

Answer

x = -1

Question 31

What is the horizontal asymptote of the rational function f(x) = (2x² + 1) / (x² - 4)?

Accepted Answer

y = 2

Answer

x = 2

Answer

y = 1

Question 32

What is the x-intercept of the function f(x) = (x - 2) / (x + 1)?

Accepted Answer

x = 2

Answer

x = 1

Answer

x = -2

Answer

x = -1

Question 33

A polynomial function has a zero at x = -3 with a multiplicity of 2. What does this tell us about the graph of the function?

Accepted Answer

The graph touches the x-axis at x = -3 and bounces back.

Answer

The graph has a vertical asymptote at x = -3.

Answer

The graph crosses the x-axis at x = -3.

Question 34

You are designing a rectangular garden with a fixed perimeter of 20 meters. What is the maximum area the garden can have?

Accepted Answer

25 square meters

Answer

50 square meters

Answer

100 square meters

Answer

10 square meters

Question 35

The cost of producing x units of a product is given by the function C(x) = 0.5x² + 10x + 50. What is the average cost of producing 10 units?

Accepted Answer

$15

Answer

$20

Answer

$25

Answer

$10